2016/03/01 by Clément Alleaume, Alleaume, Clément · 1 citation
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1603.02592
openalex publication_date 2016/03/01 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28
In this paper, we introduce a rewriting theory of linear monoidal categories.\nThose categories are a particular case of what we will define as linear (n,\np)-categories. We will also define linear (n, p)-polygraphs, a linear adapation\nof n-polygraphs, to present linear (n -- 1, p)-categories. We focus then on\nlinear (3, 2)-polygraphs to give presentations of linear monoidal categories.\nWe finally give an application of this theory in linear (3, 2)-polygraphs to\nprove a basis theorem on the category AOB with a new method using a rewriting\nproperty defined by van Ostroom: decreasingness.\n